"They had their chances to score on Monday, for some reason they didn't take them and we took the two we had," Arteta told BBC Radio Merseyside.
"In the other games this season, that hasn't been the case, so I think that was a big difference."
The Blues face Birmingham at Goodison Park on Boxing day, and Arteta admitted they would be tough to break down.
"Birmingham don't concede many chances as they are really organised and defend well," he said.
Following victory at Eastlands, Everton moved to within six points of fifth position, but remain in the bottom-half of the Premier League table in 14th spot.
And goalscoring has been a problem, with David Moyes' side managing just 20 league goals from 18 games this season, with midfielder Tim Cahill the Blues' top-scorer with nine goals this term.
Arteta added: "We've drawn too many games when we've had chances to win them.
"It's up to us - in the last game against Manchester City we had the luck we've been missing in the other games and we won."
Source: BBC Sport
Source: BBC Sport